$(50$ points$)$ For the section shown below, find:

a$.$ The centroid measured from the the upper left corner $($point $A).($Result check:

$\stackrel{}{x}=12mm\frac{,}{b}ar(y)=-2mm$

b$.$ The moments of inertia and product of inertia about the $x\text{'}-$ and $y^{\text{'}}-$axes with the origin in the centroid of the section. $($Result check: $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_{x^{\text{'}}}=1,448m{m}^4,$

$(\frac{\text{:}}{b}ar(I{)}_{y^{\text{'}}}=7,592m{m}^4\frac{,}{b}ar(I{)}_{x^{\text{'}}{y}^{\text{'}}}=1,716m{m}^4$